We posit that for melt fractions > ca. 0.3, repacking contributes significantly to the ability of the crystal columns to resist compaction. At high melt fractions, hydrodynamic interactions dominate and crystal-melt separation is accomodated by hindered settling. As melt fraction decreases, contiguity increases and eventually particle-particle interactions dominate and grain rearrangements are important (repacking dominated) (Fig. 12 ). Eventually, as melt fraction continues to decrease, the effective matrix viscosity increases rapidly as the maximum packing fraction is approached and particles no longer have any degrees of freedom for rotation and translation (Fig. 12 ). At low melt fractions (<0.3), column shortening is likely limited by GBD, or if conditions allow, some other creep mechanism. This is consistent with the results of Renner et al. (2003), who found their experiments to have a stress exponent of 1, indicating compaction in the experiments was accommodated by grain boundary diffusion-controlled creep. The rheological laws for this regime approximate grains for a variety of geometries and assume fixed center of masses (Arzt, 1982, Rudge, 2018, Takei & Holtzman, 2009). These models therefore do not account for the effects of grain rearrangements and are likely only appropriate when the melt fraction is lower than the maximum packing fraction. A transition from GBD to repacking is likely controlling the abrupt decrease in effective compaction viscosity at melt fractions of ca. 0.3 measure in Renner et al. (2003) (Fig. 12 ) and would avoid the issue of an inferred disaggregation melt fraction that is inconsistent with the centrifuge experiments.
To illustrate this point, we consider a composite GBD and repacking rheology. We use the experimental dataset C423 of Renner et al. (2003) which records a rapid increase in inferred viscosities as a function of decreasing melt fraction between melt fractions of 0.25-0.3. We use the results from the previous section to parameterize the composite rheology to model the experimental compaction rates (Fig. 13a ). The total strain rate is equivalent to the sum of strain rate for the repacking (parameters included in table 3 for olivine centrifuge experiments assuming both \(\xi_{\text{ref}}\) and\(\phi_{m}\) are material parameters) and GBD rheology. The latter is constrained by a MCMC inversion parameterized with an expression for the effective matrix viscosity expressed in eq. (20). The optimized disaggregation melt fraction in this case is a more plausible value of 0.62. The strain rates predicted by the composite rheology and that measured by experiment C423 of Renner et al. (2003) show good agreement (Fig. 13a ). Furthermore, Fig. 13billustrates that repacking accommodates the majority of compaction at melt fractions larger than the maximum packing fraction inferred from the analysis of the centrifuge experiments, while GBD controls compaction below at melt fractions below the maximum packing fraction. While we assume a single value for the maximum packing fraction, a jamming state can be reached in granular suspensions anywhere from the random lose packing to the maximum close packing. The exact transition from repacking accommodated compaction to that accommodated by GBD, therefore, may also vary within this range (for example, due to the details in how specimens with different starting melt fractions are prepared). Despite this, we find the maximum packing fractions obtained by analyzing the centrifuge experiments are commensurate with the transition in compaction rate in the Renner et al. (2003) experiments as well as the minimum trapped melt fractions inferred geochemically in the cumulates feeding high silica granites discussed by (Lee & Morton, 2015). This agreement suggests that the longevity of intrusive systems may limit melt loss at the maximum packing fraction because further melt loss would exceed the (thermal) lifespan of these bodies.